Algebra Examples

${(5 + z)}^{4}$

Step 1

Use the Binomial Theorem.

$5^{4} + 4 \cdot 5^{3} z + 6 \cdot 5^{2} z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Step 2

Simplify each term.

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Step 2.1

Raise $5$ to the power of $4$ .

$625 + 4 \cdot 5^{3} z + 6 \cdot 5^{2} z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Step 2.2

Raise $5$ to the power of $3$ .

$625 + 4 \cdot 125 z + 6 \cdot 5^{2} z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Step 2.3

Multiply $4$ by $125$ .

$625 + 500 z + 6 \cdot 5^{2} z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Step 2.4

Raise $5$ to the power of $2$ .

$625 + 500 z + 6 \cdot 25 z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Step 2.5

Multiply $6$ by $25$ .

$625 + 500 z + 150 z^{2} + 4 \cdot 5 z^{3} + z^{4}$

Step 2.6

Multiply $4$ by $5$ .

$625 + 500 z + 150 z^{2} + 20 z^{3} + z^{4}$